Polytope of Type {5,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,12}*1920c
if this polytope has a name.
Group : SmallGroup(1920,241004)
Rank : 3
Schlafli Type : {5,12}
Number of vertices, edges, etc : 80, 480, 192
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 5
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,6}*960
   32-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5,15)( 7, 8)( 9,30)(11,16)(12,17)(13,25)(14,19)(18,29)(20,31)
(21,28)(22,27)(23,32)(24,26);;
s1 := ( 2, 3)( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,21)(17,20)(18,22)(19,23)
(24,28)(25,26)(27,31)(29,30);;
s2 := ( 1, 2)( 3,31)( 4,20)( 5,16)( 6,10)( 7,32)( 8,23)( 9,19)(11,15)(13,21)
(14,30)(18,29)(22,27)(25,28);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(32)!( 3, 4)( 5,15)( 7, 8)( 9,30)(11,16)(12,17)(13,25)(14,19)(18,29)
(20,31)(21,28)(22,27)(23,32)(24,26);
s1 := Sym(32)!( 2, 3)( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,21)(17,20)(18,22)
(19,23)(24,28)(25,26)(27,31)(29,30);
s2 := Sym(32)!( 1, 2)( 3,31)( 4,20)( 5,16)( 6,10)( 7,32)( 8,23)( 9,19)(11,15)
(13,21)(14,30)(18,29)(22,27)(25,28);
poly := sub<Sym(32)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2 >;

References : None.
to this polytope